One of the most important tools in our paper is the algebraic Gauss-Manin connection. It was first introduced in the paper [1]}, by Katz and Oda. They defined the Gauss-Manin connection for any smooth morphism \(\pi : X\rightarrow S\)  of smooth schemes (in other words, a family over \(S\) ). Roughly, it formalizes the notion of differentiating with respect to the parameters of a family. They consider the algebraic de Rham cohomology of the family, which is the hyperderived sheaf
\(\mathcal {H}_{dR}^m(X/S):=R^m\pi _*(\Omega ^{\bullet }_{X/S})\) 
